Clinical study

The fluorescence signal was measured during the occlusive treatment in chapter 7. The char- acteristic red light produced as a result of blue excitation light was collected every 20 minutes for a total of three hours. Statistical modelling showed a linear trend between the fluores- cence signal and the occlusive time. A more detailed description of the study can be found in chapter 7. To be able to gain more understanding of the production of PpIX within the tumour lesions the parameters in equation 4.9 were adjusted to generate the set of parameters that best fit the linear model (table 4.4). The peak of the fluorescence signal (from the theoretical results) as it changed with time for these sets (set B1 and B2, table 4.4) and the statistical model compared successfully as shown in figures 4.11 and 4.12. To determine if these sets of parameters are plausible further investigations were carried out. Using parameters B1 and B2 in table 4.4, the light treatment was simulated and the PDD was determined. For set B1 treatment deaths of less than 0.5 mm were achieved, which can be seen in figure 4.13. For set B2 the treatment PDD is displayed in figure 4.14, where the applied threshold is higher than the achieved PDD. The concentration profiles generated by sets B1 and B2 (table 4.4) at 30, 60 and 180 min after cream application are displayed in figure 4.15. The results indicate that the distribution of PpIX reached only superficial layers where the overall concentration is low compared to sets 1-8 in table 4.2.

4.4. Results Clinical result Theoretical result 0 50 100 150 Time [min] 0.0 0.2 0.4 0.6 0.8 1.0 Normalised Fluorescence

Figure 4.10: Figure showing how the fluorescence signal (red) changes with time for the first set of parameters (set 1) in table 4.2. The linear model (black) corresponds to the clinical results. Clinical result Theoretical result 0 50 100 150 Time [min] 0.0 0.2 0.4 0.6 0.8 1.0 Normalised Fluorescence

Figure 4.11: Figure showing how the fluorescence signal (red) changes with time for the first set of parameters (set B1) in table 4.4. The linear model (black) corresponds to the clinical results. This shows one of the best combination of parameters that were found to match the clinical results.

Clinical result Theoretical result 0 50 100 150 Time [min] 0.0 0.2 0.4 0.6 0.8 1.0 Normalised Fluorescence

Figure 4.12: Figure showing how the fluorescence signal (red) changes with time for the second set of parameters (set B2) in table 4.4. The linear model (black) corresponds to the clinical results. This shows one of the best combination of parameters that were found to match the clinical results.

Aktilite Daylight (clear) Daylight (overcast) 0 1 2 3 4 5 Depth [mm] 0.1 1.0 10.0 Photodynamic Dose [10 18 photons /cm 3 ]

Figure 4.13: Figure showing the photo-toxicity as it changes with depth after 75J cm 2 of delivered light dose where the parameters in set B1 (table 4.4) were adopted. The figure shows the same light conditions as previously been investigated. The figure shows a relatively low penetration compared to the uniform case investigated in previous chapter (chapter 3).

4.4. Results Aktilite Daylight (clear) Daylight (overcast) 0 1 2 3 4 5 Depth [mm] 0.1 1.0 10.0 Photodynamic Dose [10 18 photons /cm 3 ]

Figure 4.14: Figure showing the photo-toxicity as it changes with depth after 75J cm 2 of delivered light dose where the parameters in set B2 (table 4.4) were adopted. The model presented indicates that this set of parameters results in a reasonable treatment depth, how-

ever the validity of the relaxation time⌧pcould be argued.

Set B1 Set B2 30 min 1 h 3 h 0 1 2 3 4 5 Depth [mm] 0.01 0.10 1.00 10.00 Number density [10 14 cm − 3 ]

Figure 4.15: Figure showing the concentration after 30, 60 and 180 min of incubation time (no light interaction) for set B1 and B2 from table 4.4. These parameters produced the fluorescent signal from the MCRT model that matched the clinical set most favourably.

4.5 Discussion

It is clear from the investigation performed here, that without accurate knowledge of the different parameters: A,⌧_pand D in equation 4.9, it is difficult to generate an appropriate distribution. Therefore the parameter exploration is important in terms of determining the contribution from the different parameters. During the light exposure the concentration re- duces due to photobleaching, as demonstrated in figure 4.6. For the two daylight cases (clear and overcast) there is additional PpIX production during the light illumination. For clear con- ditions during daylight PDT figure 4.6 b demonstrates a large drop in concentration during the initial 10 J cm 2 for the non-uniform situation. This drop is larger than the drop for the same light dose for overcast conditions during daylight PDT (non-uniform case), shown in figure 4.6 c. Due to the difference in irradiance between these two weather conditions, the time it takes to deliver the same light dose of 10 J cm 2 _{corresponds to 2 min (clear) and 21} min (overcast). During this time, there is a larger amount of additional PpIX being produced, for the overcast situation compared to the clear situation. This explains the overall larger PpIX concentrations during overcast conditions.

The first set of parameters (set 1 in table 4.2) is what is believed to be a reasonable assumption of the parameters. For this reason this set is the most discussed and explored in this chapter. The results shown in figure 4.7 indicates treatment depths similar to the uniform case described in chapter 3, after a delivered light dose of 75 J cm 2_{during conventional PDT.} This indicates that these parameters result in realistic treatment depths. For daylight PDT the overcast treatment depth is larger than for the clear conditions when considering a total light dose of 75 J cm 2. This feature is consistent for all parameters investigated and is explored in more detail in Appendix B. However when comparing the same treatment time (2.5 hours), the clear conditions results in deeper penetration. This is explained by the increased light dose delivered during 2.5 hours of illumination during clear (370 J cm 2_{) conditions compared to} overcast (75 J cm 2) conditions. This is graphically demonstrated in figure 4.8.

Even though the treatment depths are varied, the fluorescence signal does not in general vary as much (table 4.3). When the relaxation time⌧_p, in sets 5 and 6 in table 4.2, is changed

the evolution of the fluorescence signal does not change from the initial set of parameters (set 1) however there is a change in effective treatment depth. For the situations where the fluorescence signal carries a closer resemblance to the linear trend, this resulted overall, in

4.5. Discussion

more superficial treatment depths. The two sets of parameters that were found where the fluorescence signal favourably correlated to the linear trend (figure 4.11 and 4.12), resulted in superficial treatment depths as shown in figures 4.13 and 4.14. Even though the applied toxic threshold is an approximation, the light penetration for these two sets of parameters is confined to superficial layers. Hence there is reason to believe that these sets of parameters are not appropriate. In addition the relaxation time⌧pfor set B2 in table 4.4 is approximately 0.5 s. This can be argued to be unreasonable since this would correspond to a faster clearance of PpIX than has previously been suggested in the literature[188]. Even though there might be other sets of parameters that match the linear trend as well as results in deeper light penetration these have not yet been found in the work presented here.

There are several potential explanations to why the set of parameter that matched the linear trend best, resulted in unreasonably low penetration depths. First of all the model developed in this chapter might not be sophisticated enough to be able to match the clinical results with the theoretical models. By simplifying the process of accumulating PpIX in the tumour, important information might be lost. It has been suggested in the literature that dose dependent rate equations should be used instead of first order kinetics when considering the production of PpIX since the conversion is controlled by an enzyme reaction. Due to the rate limitation of the process of producing PpIX, it is potentially important to include such aspects within the model[173]. However limited knowledge of these processesin vivo, discourages the application of such methods within the model presented here. As will be discussed in chapter 6, there is a possibility that the clinical data was affected by the degree of the surface preparation. By applying a deep curettage some of the measurements would be affected by the amount of blood produced as well as by the thin lesions remaining. Surface preparations are necessary to enable the cream to penetrate however the degree of curettage is varied between different institutes. Other aspects of the clinical study, might also have affected the measurements, such as exposure to light every 20 min. Further discussion of these issues may be found in chapter 6. For this reason alternative trends should not be discarded for future extended studies.

It is believed that the initial set, set 1 in table 4.2, is the most reasonable set of data strengthened by reasonable treatment depths. However these are approximations and the fluorescence signal generated from the models shows in figure 4.10 a steep increase at early times before plateauing. A possible explanation to the reason why the clinical results and the

theoretical results do not coincide is the tumour depth. The curettage associated with the clinical study could result in a shallow tumour depth. If the tumour is very superficial, a set of parameters resulting in a linear fluorescence trend (set B1 and B2) could be motivated. See chapter 6 for a further discussion of the level of curettage. Future developments have to include extension of the theoretical model as well as additional clinical studies where the level of curettage is considered.

By including a distribution of PpIX which changes both temporally and spatially, a more accurate theoretical representation of PDT may be obtained. By increasing the appropriate- ness of the model more accurate information can be gained from the resulting simulations. However, in the model developed here, several aspects of the PpIX production have not been considered for the sake of simplicity. It was assumed that the PpIX did not diffuse from the location where it is produced. It was also assumed that the concentration gradient of MAL molecules was not affected by the production of PpIX or photobleaching. To include these processes, a more complex model would be required where more parameters would have to be assumed and approximated. Additionally it was also assumed that the light penetra- tion was not affected by the presence of cream on the surface of the lesion. If the optical properties of the cream were known, a thin layer of cream could be added to the simula- tion. However, due to lack of this information, it was not included in the model. Future developments of the model should consider the steps discussed above as well as the permeab- ility of the cream through the skin. Here the permeability is ignored since it was assumed that the stratum corneum was broken up with a reduced functionality in the region of the tumour [53, 65, 174, 175]. It was additionally approximated that there was no difference between MAL or ALA based creams. Other aspects of the model that have not been included are the non-uniformity in the lateral direction (along the surface) as well as between different types of tumour positioned on different locations of the body_[69_].

The diffusion model presented here is a step towards a more accurate representation of the different treatment modalities. By adopting reasonable parameters for A, ⌧_p, and D in

equation 4.9 such as the ones suggested in set 1 in table 4.2, the model indicates that the treatment depth is not only limited by the light penetration but also by the drug diffusion and PpIX production rate. These are important factors to consider when calculating and optimising PDT dosimetry. The work presented here is a step towards further exploring the limitations and potential of daylight PDT which can be a useful technique for situations when limited

4.6. Conclusion

resources are in place.

4.6 Conclusion

The incubation time associated with different treatment modalities results in different initial distributions of the photosensitive molecule PpIX. A non-uniform distribution of PpIX was investigated where a model was developed which depends on both the distance from the sur- face as well as the time passed since prodrug application. The main challenges are the limited knowledge about the cream diffusion and PpIX production which forces several assumptions and approximations. The work presented here explores the effect that these parameters have on the distribution of PpIX and the associated treatment depths. By including a non-uniform distribution of PpIX a more accurate representation of PDT was achieved. The results suggest that the treatment depths associated with PDT are not only limited by the penetration of the light but also by the penetration of the prodrug as well as the production of PpIX. Even though further investigation is required to establish the distribution parameters, the work presented here is a stepping stone towards more accurate theoretical simulations of PDT during different treatment conditions. Including a time dependent PpIX production model is key in driving the theoretical simulations of light based therapies forward.

5

Light distribution modelling of skin ageing and

different skin types

5.1 Summary

It is important to adopt appropriate optical properties when modelling light distribution through skin tissue. This chapter discusses the techniques of generating the optical properties adopted throughout this thesis. By appropriately adjusting the optical properties and compos- ition of a multi-layered skin phantom, different ages and skin types were represented. The results demonstrate the effect that different optical properties have on the distribution and penetration of light. The developed model shows that the light penetration increases with age and reduces with increasing skin type classification number. The results also indicate that daylight photodynamic therapy (PDT) is more affected by ageing and level of pigmentation compared to conventional PDT methods.

volume 9531) "3D Monte Carlo radiation transfer modelling of photodynamic therapy" (2015) [189].